Voozh

A192270

Pseudo anti-perfect numbers.

5, 7, 8, 10, 17, 22, 23, 31, 32, 33, 35, 38, 39, 41, 45, 49, 52, 53, 56, 59, 60, 63, 67, 68, 70, 71, 72, 73, 74, 76, 77, 81, 82, 83, 85, 88, 94, 95, 98, 101, 102, 103, 104, 105, 108, 109, 110, 112, 115, 116, 117, 122, 123, 127, 129, 130, 137, 138, 143, 144, 147, 148, 149, 150, 151, 154, 157, 158, 162, 164, 165, 167, 171, 172, 175, 176, 178, 179, 182, 185

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OFFSET

1,1

COMMENTS

A pseudo anti-perfect number is a positive integer which is the sum of a subset of its anti-divisors. By definition, anti-perfect numbers (A073930) are a subset of this sequence.

Prime pseudo anti-perfect numbers begin: 5, 7, 17, 23, 31, 41, 53, 59, 67, 71, 73, 83, 101, 103, 109, 127, 137, 149, 151, 157, 167, 179, .... - Jonathan Vos Post, Jul 09 2011

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1000

EXAMPLE

39 is pseudo anti-perfect because its anti-divisors are 2, 6, 7, 11, 26 and the subset of 2, 11, and 26 adds up to 39.

MAPLE

with(combinat);

P:=proc(i)

local a, k, n, S;

for n from 1 to i do

a:={};

for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;

S:=subsets(a);